[CM] numerics.scm

```Hi,

For numerics.scm, these seem useful.  Most of them I can evaluate, but the four
polynomials (xxx) I cannot seem to figure what it wants.  Wondering if anyone
might have success or ideas about those guys?```
```

Thank You,

Jim

(factorial 6) -> 720
(binomial 4 2) -> 6
(n-choose-k 10 2) ->45
(plgndr 6 .2 -1) ->2.261952
(legendre-polynomial 1 4);XXX -> argument 1, #f, is boolean but should be a
number
(legendre 3 4) ->154.0
(gegenbauer 3 4) -> 0.5625693058216614
(chebyshev-polynomial 2 4)  ;XXX -> argument 1, #f, is boolean but should be a
number
(chebyshev 2 4) -> 31.0
hermite-polynomial 1 3)  ;XXX -> argument 1, #f, is boolean but should be a
number
(hermite 1 3) ->6.0
(laguerre-polynomial 3 1)  ;XXX -> argument 1, #f, is boolean but should be a
number
(laguerre 1 4 ) -> -3.0
(Si 10)->1.658347864640153
(Ci 10)->-0.04545628800337046
(sin-m*pi/n 1 9) ->(let ((ex (sqrt 3/4))) (/ (- (expt (+ (sqrt (- 1 (* ex ex)))
(* 0+1i ex)) (/ 1 3)) (expt (- (sqrt (- 1 (* ex ex))) (* 0+1i ex)) (/ 1 3)))
0+2i))
(show-digits-of-pi-starting-at-digit 2.0)->
position = 2.000000e+00
fraction = 1.247719318987069
hex digits =  "3F6A8885A3       "
" position = 2.000000e+00
fraction = 1.247719318987069
hex digits =  \"3F6A8885A3       \"
"

```
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• [CM] numerics.scm James Hearon